Sin 30 Degrees

The value of sin 30 degrees is 0.5. Sin 30 degrees in radians is written as sin (30° × π/180°), i.e., sin (π/6) or sin (0.523598. . .). In this article, we will discuss the methods to find the value of sin 30 degrees with examples.

• Sin 30°: 0.5
• Sin 30° in fraction: 1/2
• Sin (-30 degrees): -0.5
• Sin 30° in radians: sin (π/6) or sin (0.5235987 . . .)

What is the Value of Sin 30 Degrees?

The value of sin 30 degrees in decimal is 0.5. Sin 30 degrees can also be expressed using the equivalent of the given angle (30 degrees) in radians (0.52359 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 30 degrees = 30° × (π/180°) rad = π/6 or 0.5235 . . .
∴ sin 30° = sin(0.5235) = 1/2 or 0.5

Explanation:

For sin 30 degrees, the angle 30° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 30° value = 1/2 or 0.5
Since the sine function is a periodic function, we can represent sin 30° as, sin 30 degrees = sin(30° + n × 360°), n ∈ Z.
⇒ sin 30° = sin 390° = sin 750°, and so on.
Note: Since, sine is an odd function, the value of sin(-30°) = -sin(30°).

Methods to Find Value of Sin 30 Degrees

The sine function is positive in the 1st quadrant. The value of sin 30° is given as 0.5. We can find the value of sin 30 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 30 Degrees Using Unit Circle

To find the value of sin 30 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 30° angle with the positive x-axis.
• The sin of 30 degrees equals the y-coordinate(0.5) of the point of intersection (0.866, 0.5) of unit circle and r.

Hence the value of sin 30° = y = 0.5

Sin 30° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 30 degrees as:

• ± √(1-cos²(30°))
• ± tan 30°/√(1 + tan²(30°))
• ± 1/√(1 + cot²(30°))
• ± √(sec²(30°) - 1)/sec 30°
• 1/cosec 30°

Note: Since 30° lies in the 1st Quadrant, the final value of sin 30° will be positive.

We can use trigonometric identities to represent sin 30° as,

• sin(180° - 30°) = sin 150°
• -sin(180° + 30°) = -sin 210°
• cos(90° - 30°) = cos 60°
• -cos(90° + 30°) = -cos 120°

☛ Also Check:

• sin 90 degrees
• sin 15 degrees
• sin 18 degrees
• sin 220 degrees
• sin 750 degrees
• sin 33 degrees

FAQs on Sin 30 Degrees

What is Sin 30 Degrees?

Sin 30 degrees is the value of sine trigonometric function for an angle equal to 30 degrees. The value of sin 30° is 1/2 or 0.5.

How to Find the Value of Sin 30 Degrees?

The value of sin 30 degrees can be calculated by constructing an angle of 30° with the x-axis, and then finding the coordinates of the corresponding point (0.866, 0.5) on the unit circle. The value of sin 30° is equal to the y-coordinate (0.5). ∴ sin 30° = 0.5.

How to Find Sin 30° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 30° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(30°))
• ± tan 30°/√(1 + tan²(30°))
• ± 1/√(1 + cot²(30°))
• ± √(sec²(30°) - 1)/sec 30°
• 1/cosec 30°

☛ Also check: trigonometry table

What is the Value of Sin 30° in Terms of Cosec 30°?

Since the cosecant function is the reciprocal of the sine function, we can write sin 30° as 1/cosec(30°). The value of cosec 30° is equal to 2.

What is the Value of Sin 30 Degrees in Terms of Cot 30°?

We can represent the sine function in terms of the cotangent function using trig identities, sin 30° can be written as 1/√(1 + cot²(30°)). Here, the value of cot 30° is equal to 1.73205.